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Methyl Cation Affinities of Neutral and Anionic Maingroup-Element Hydrides: Trends Across the Periodic Table and Correlation with Proton Affinities R. Joshua Mulder, Ce´lia Fonseca Guerra, and F. Matthias Bickelhaupt* Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Scheikundig Laboratorium der Vrije UniVersiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, Netherlands ReceiVed: April 3, 2010; ReVised Manuscript ReceiVed: June 4, 2010
We have computed the methyl cation affinities in the gas phase of archetypal anionic and neutral bases across the periodic table using ZORA-relativistic density functional theory (DFT) at BP86/QZ4P//BP86/TZ2P. The main purpose of this work is to provide the methyl cation affinities (and corresponding entropies) at 298 K of all anionic (XHn-1-) and neutral bases (XHn) constituted by maingroup-element hydrides of groups 14-17 and the noble gases (i.e., group 18) along the periods 2-6. The cation affinity of the bases decreases from H+ to CH3+. To understand this trend, we have carried out quantitative bond energy decomposition analyses (EDA). Quantitative correlations are established between the MCA and PA values. 1. Introduction Designing new and optimizing existing approaches and routes in chemical synthesis requires knowledge of the thermochemistry involved in the targeted reactions. In contrast with proton affinities (PA), methyl cation affinities (MCA) have received less attention in the literature. Yet, overall reaction enthalpies and reaction barriers are related to the MCA as soon as a methyl cation is transferred somewhere along the cascade of elementary steps of a reaction mechanism, for example, in nucleophilic substitutions.1,2 This thermochemical quantity is defined as the enthalpy change associated with dissociation of the methylcation complex of the anionic or neutral base, as shown in eqs 1 and 2, respectively:
BCH3 f B- + CH+ 3:
∆H ) MCA
(1)
+ BCH+ 3 f B + CH3 :
∆H ) MCA
(2)
In this article, we focus on the MCA of anionic and neutral maingroup-element hydrides in the gas-phase. Gas-phase MCAs are obviously directly applicable to gas-phase chemistry, but they are also relevant for condensed-phase reactions, such as, SN2 substitution in which a methyl cation is transferred in a concerted mechanism. On one hand, they reveal the intrinsic MCA of the different maingroup-element hydrides involved, and thus, they shed light on how this property is affected by the solvent. On the other hand, they can serve as a universal, solvent-independent framework of reference, from which the actual values of a species in solution can be obtained using, for example, an empirical correction for the particular solvent under consideration (such solvation corrections are, however, beyond the scope of the present work).3,4 The present study has three objectives. First, we set up a complete description at BP86/QZ4P//BP86/TZ2P of the MCA of the anionic maingroup-element hydrides (XHn-) of group 14-17 and periods 2-6 and the neutral maingroup-element * To whom correspondence should be addressed. Fax: +31-20-59 87617. E-mail:
[email protected].
hydrides (XHn) of group 15-17 and the noble gases, that is, group 18, and periods 1-6. In addition to the MCA values of all bases (∆acidH298), we also report the corresponding 298 K reaction entropies (∆acidS298, provided as -T∆acidS298) and 298 K reaction free energies (∆acidG298). Second we wish to compare the calculated MCA with PA; the MCA is known to correlate with the PA,5-9 and this correlation is further investigated here. Third, we want to gain a deeper understanding in the trends using bond-energy decomposition analyses. 2. Methods 2.1. Basis Sets. All calculations were performed with the Amsterdam Density Functional (ADF) program developed by Baerends and others.10,11 Molecular orbitals (MOs) were expanded using two different large uncontracted sets of Slatertype orbitals: TZ2P and QZ4P.12 The TZ2P basis set is of triple-ζ quality, augmented by two sets of polarization functions (d and f on heavy atoms; 2p and 3d sets on H). The QZ4P basis, which contains additional diffuse functions, is of quadruple-ζ quality, augmented by four sets of polarization functions (two d and f on heavy atoms; two 2p and two 3d sets on H). Core electrons (e.g., 1s for second period, 1s2s2p for third period, 1s2s2p3s3p for fourth period, 1s2s2p3s3p3d4s4p for fifth period, and 1s2s2p3s3p3d4s4p4d for sixth period) were treated by the frozen core approximation.11 An auxiliary set of s, p, d, f, and g Slatertype orbitals was used to fit the molecular density and to represent the coulomb and exchange potentials accurately in each self-consistent field (SCF) cycle. Scalar relativistic corrections were included self-consistently using the zeroth order regular approximation (ZORA).13 2.2. Density Functional. Energies, geometries and vibrational frequencies were calculated using the local density approximation (LDA; Slater exchange14 and VWN15 correlation) with gradient corrections16,17 due to Becke (exchange) and Perdew (correlation) added self-consistently. This is the BP86 density functional that is one of the three best DFT functionals for the accuracy of geometries,18 with an estimated unsigned error of 0.009 Å in combination with the TZ2P basis set. In previous studies,19,20 on the PA of anionic and neutral species, the energies of a range of DFT functionals were compared, to estimate the influence of the choice of DFT functional. The
10.1021/jp103011k 2010 American Chemical Society Published on Web 06/24/2010
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BP86 functional emerged as one of the best functionals. Geometries were optimized using analytical gradient techniques until the maximum gradient component was less than 1.0 × 10-5 atomic units (see Table S5 in the Supporting Information). Vibrational frequencies were obtained through computation of the analytical Hessian matrix. 2.3. Energy Decomposition Analysis. The overall bond energy ∆E between base B(-) and CH3+ is made up of two major components (eq 2)21,22
∆E ) ∆Eprep + ∆Eint
(3)
In this formula, the preparation energy ∆Eprep is the amount of energy required to deform the separate base and methyl cation from their equilibrium structure to the geometry that they acquire in the overall complex BCH3(+). The interaction energy ∆Eint corresponds to the actual energy change when the geometrically deformed base and methyl cation are combined to form the overall complex. It is analyzed in the bonded model systems in the framework of the Kohn-Sham MO model using a decomposition of the bond into electrostatic interaction, Pauli repulsion, and (attractive) orbital interactions (eq 4).
∆Eint ) ∆Velstat + ∆EPauli + ∆Eoi
(4)
The term ∆Velstat corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the prepared (i.e., deformed) base and methyl cation. This term is usually attractive. The Pauli repulsion, ∆EPauli, comprises the destabilizing interactions between occupied orbitals. Note that it is this Pauli term that is responsible for the steric repulsion. The orbital interaction, ∆Eoi, in any MO model, and therefore also in Kohn-Sham theory, accounts for charge transfer (i.e., donor-acceptor interactions between occupied orbitals on one moiety with unoccupied orbitals of the other, including the HOMO-LUMO interactions) and polarization (empty/occupied orbital mixing on one fragment due to the presence of another fragment). 2.4. Thermochemistry. Enthalpies at 298.15 K and 1 atm (H298) were calculated from electronic bond energies (E), vibrational frequencies, and moments of inertia using standard thermodynamic relations, proceeding from the partition functions for an ideal gas,23 according to eq 5:
∆H298 ) ∆E + ∆Etrans,298 + ∆Erot,298 + ∆Evib,0 + ∆(∆Evib,0)298 + ∆(pV) (5) Here, ∆Etrans,298, ∆Erot,298, and ∆Evib,0 are the differences between the base-methyl cation complex and the separate base and methyl cation in translational, rotational, and zero-point vibrational energy, respectively; ∆(∆Evib,0)298 is the change in the vibrational energy difference as one goes from 0 to 298.15 K. The vibrational energy corrections are based on our frequency calculations. The molar work term ∆(pV) is (∆n)RT; ∆n ) +1 for one base-methyl cation complex dissociating into the separate base and methyl cation. Thermal corrections for the electronic energy are neglected. Entropy corrections (∆S298) were again computed proceeding from the partition functions for an ideal gas. 3. Results and Discussion 3.1. Evaluation of the Approach. We begin with an evaluation of the performance of our computational approach.
TABLE 1: Computed and Experimental Methyl Cation Affinities (in kcal/mol) base
BP86/TZ2Pa
BP86/QZ4Pb
experimentalc
CH3NH2OHFSHClBrINH3 H 2O HBr HCl MAD wrt expd MD wrt expe
320.3 304.2 288.1 270.0 252.8 234.2 224.8 218.6 108.2 70.0 60.6 54.8 5.7 5.7
315.4 297.5 281.1 265.3 251.6 231.4 224.2 217.9 108.3 70.4 60.6 54.8 3.4 3.4
315.4 ( 1.5 295.4 ( >0.5 278.2 ( >2.9 261.6 ( >0.4 247.4 ( >0.6 227.3 ( 0.6 219.4 ( 0.7 213.5 ( 0.7 105.7 ( >0.6 66.8 ( >0.5 55.4 51.6
a This work, computed at BP86/TZ2P//BP86/TZ2P. b This work, computed at BP86/QZ4P//BP86/TZ2P. c From refs 5, 24, and 25. d Mean absolute deviation with respect to experiment. e Mean deviation with respect to experiment.
To this end, we have computed the methyl cation affinities (MCA ) ∆H298) for a series of 7 anionic and 4 neutral bases, shown in Table 1, for which experimental values are available.5,24,25 This series of bases covers MCA values ranging from 54.8 for HCl through 315.4 kcal/mol for CH3-. Table 1 compares the effect of carrying out the DFT BP86 calculations with the TZ2P versus the larger QZ4P basis set. At BP86/TZ2P, we find MCA values with a mean absolute deviation (MAD) with respect to the experimental values of 5.7 kcal/mol and a mean deviation (MD) of also 5.7 kcal/ mol. Thus, all calculated MCA values are consistently larger than the experimental ones. A large improvement can be achieved by going from the TZ2P tot the QZ4P basis set. The QZ4P basis set is not only more flexible and better polarized, it also contains more diffuse functions. One may, therefore, expect an improved description of reaction 1 in which we go from a neutral species BCH3 to a negatively charge B- and a positively charged CH3+. In particular, the description of the expanding density (“breathing orbitals”) at the nucleophilic center (e.g., nitrogen in CH3NH2 and NH2-) benefits from going from the TZ2P to the QZ4P basis sets. Single-point energy calculations were done at BP86/QZ4P using the BP86/TZ2P geometries. At this level of theory, that is, at BP86/QZ4P// BP86/TZ2P, we achieve a significant improvement of the MAD and MD, which drops to 3.5 kcal/mol relative to the experimental values. The overestimation of the MCA must be kept in mind when applying our results to experimental situations. Trends, however, are less affected by the consistent overestimation of the MCA values. We have verified that neither the geometry nor the enthalpy corrections differ significantly if the geometries were also optimized using the QZ4P basis set. Thus, the full BP86/QZ4P// BP86/QZ4P energies differ by merely 0.06 kcal/mol or less compared to the BP86/QZ4P// BP86/TZ2P energies (tested for NH2-, F- and H2O), whereas the enthalpy corrections differ by only 0.05 kcal/mol or less (tested for NH2- and H2O). In conclusion, BP86/QZ4P//BP86/TZ2P emerges as a reliable approach for studying trends in the basicity of anionic and neutral bases in the following sections. 3.2. Methyl Cation Affinities of Anionic MaingroupElement Hydrides. Our methyl cation affinities at 298 K (∆acidH298), the corresponding entropies ∆acidS298 (provided as
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TABLE 2: Thermodynamic MCA Properties (in kcal/mol) for Anionic Maingroup-Element Hydrides XHn- at 298 Ka group 14 period P2 P3 P4 P5 P6 a
base -
CH3 SiH3GeH3SnH3PbH3-
∆H 315.4 281.6 265.1 250.4 231.5
-T∆S -10.8 -10.2 -10.1 -9.6 -9.4
group 15 ∆G 304.6 271.4 255.0 240.8 222.1
base -
NH2 PH2AsH2SbH2BiH2-
∆H 297.5 271.5 262.9 254.8 251.1
-T∆S -9.6 -9.6 -9.5 -9.2 -9.1
group 16 ∆G 287.9 261.9 253.4 245.6 242.0
base -
OH SHSeHTeHPoH-
∆H 281.1 251.6 243.4 235.9 233.3
-T∆S -8.6 -8.5 -8.3 -8.0 -8.0
group 17 ∆G
base
∆H
-T∆S
∆G
272.6 243.2 235.0 228.0 225.4
-
265.3 231.4 224.2 217.9 216.5
-7.8 -7.5 -7.4 -7.2 -7.2
257.5 223.9 216.8 210.7 209.3
F ClBrIAt-
Computed at BP86/QZ4P//BP86/TZ2P for the reaction CH3XHn-1 f CH3+ + XHn-1-.
Figure 1. Methyl cation affinities MCA (at 298 K) of the anionic maingroup-element hydrides XHn- of groups 14-17 and periods 2-6 (P2-P6) computed at BP86/QZ4P//BP86/TZ2P (upper), and the corresponding proton affinities PA (at 298 K), computed at BP86/ QZ4P//BP86/TZ2P (lower).
-T∆acidS298 values) and reaction free energies ∆acidG298 of all anionic maingroup-element hydrides of groups 14-17 and periods 2-6 are summarized in Table 2 and Figure 1. The MCA decreases from 315 to 298 to 281 to 265 kcal/ mol along the anionic second-period bases CH3-, NH2-, OH-, and F-, respectively (see Table 2 and Figure 1, upper). In each of the groups (14-17) the MCA decreases if one descends the periodic table. The largest reduction in MCA occurs from the second to the third period. In group 14, for example, the MCA decreases from 315 to 282 to 265 to 250 to 232 kcal/mol along CH3-, SiH3-, GeH3-, SnH3-, and PbH3- (see Table 2). Interestingly, the changes in MCA descending group 14 are significantly larger than in the other groups, 15-17. Thus, as can be seen in Figure 1, upper, the
trend of a monotonic decrease in MCA along the second period (P2) and already to a lesser extent, the third and fourth period (P3 and P4) changes for the fifth and sixth period (P5 and P6) into a trend where the MCA first increases from group 14 to 15 and then decreases again along groups 16 to 17. Our bonding analyses show that the above trends in MCA are determined by the electrostatic attraction ∆Velstat (which becomes weaker for larger bond distances) and, in most cases, the donor-acceptor orbital interactions ∆Eoi (see Table S1 in the Supporting Information). The corresponding reaction entropies yield a relatively small (but not entirely constant) contribution -T∆acidS298 of -11 to -7 kcal/mol for 298K. As a consequence, the Gibbs free energies ∆acidG298 show the same trends as the corresponding MCA values (Table 2). The above trends in MCAs of anionic maingroup-element hydrides XHn-1- strongly resemble those in PAs that we found previously (compare Figure 1, upper with lower).19 The most important difference is that MCA values are consistently lower than the corresponding PA. Our bonding analyses show that the single most important reason that MCAs are weaker than the corresponding PAs is the complete absence of any steric (Pauli) repulsion ∆EPauli in the latter case, as the proton has no electrons that could cause Pauli repulsion with the electrons of the base (compare Tables S1 and S2 in the Supporting Information). At variance, the methyl cation does have valence electrons. This steric repulsion that results from overlap with the occupied orbitals of the base (notably its lone pair) shows up, among others, in a ∆EPauli term of 115-286 kcal/mol (see Table S1). 3.3. Methyl Cation Affinities of Neutral MaingroupElement Hydrides. Our methyl cation affinities at 298 K (∆acidH298), the corresponding entropies ∆acidS298 (provided as -T∆acidS298 values) and reaction free energies ∆acidG298 of all neutral maingroup-element hydrides of groups 15-17 and the noble gases (i.e., group 18) for periods 1-6 are summarized in Table 3 and Figure 2. The MCA decreases from 108 to 71 to 36 to 5 kcal/mol along the neutral second-period bases NH3, OH2, FH, and Ne, respectively (Table 3). A striking change occurs from group 15 to the higher groups. Descending group 15, the MCA decreases. Descending one of the other groups (16-18), the MCA increases, as one can see in Figure 2 (upper). This causes the trend of a monotonic decrease in MCA along the second period (P2) and, to a lesser extent the third and fourth periods (P3, P4) to change into a trend for the fifth and sixth periods (P5, P6), where the MCA along a period increases from group 15 to 16 and then decreases again along groups 16, 17, and 18. In group 15, for example, the MCA changes from 108 to 109 to 97 to 94 to 80 kcal/mol along NH3, PH3, AsH3, SbH3, and BiH3, whereas in group 16 the MCA increases from 71 to 88 to 89 to 96 to 97 kcal/mol along OH2, SH2, SeH2, TeH2, and PoH2 (Table 3). The corresponding reaction entropies for 298
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TABLE 3: Thermodynamic MCA Properties (in kcal/mol) for Neutral Maingroup-Element Hydrides XHn at 298 Ka group 15
group 16
group 17
group 18
period
base
∆H
-T∆S
∆G
base
∆H
-T∆S
∆G
base
∆H
-T∆S
∆G
base
∆H
-T∆S
∆G
P1 P2 P3 P4 P5 P6
NH3 PH3 AsH3 SbH3 BiH3
108.3 109.1 96.4 94.3 79.6
-10.3 -10.3 -10.1 -8.7 -9.3
98.0 98.8 86.3 85.6 70.4
OH2 SH2 SeH2 TeH2 PoH2
70.5 87.5 88.9 95.5 97.4
-9.3 -9.6 -9.5 -9.1 -9.1
61.3 77.9 79.4 86.4 88.3
FH ClH BrH IH AtH
35.6 54.8 60.7 70.1 74.1
-8.0 -8.2 -8.0 -8.0 -7.9
27.6 46.6 52.6 62.1 66.2
He Ne Ar Kr Xe Rn
3.6 4.7 23.7 33.0 45.3 51.3
-7.0 -6.8 -7.2 -7.1 -7.1 -7.1
-3.4 -2.1 16.6 25.9 38.2 44.3
a
Computed at BP86/QZ4P//BP86/TZ2P for the reaction CH3XHn+ f CH3+ + XHn.
Figure 3. Plot of methyl cation affinities MCA versus proton affinities PA in the gas phase (at 298K), computed at BP86/QZ4P//BP86/TZ2P (see eq 6).
in eq 6, together with the correlation coefficient R and the standard deviation SD for 41 data points:
MCA ) 0.895 PA - 61.82: f R2 ) 0.995, SD ) 7.3 (6)
Figure 2. Methyl cation affinities MCA (at 298 K) of the neutral maingroup-element hydrides of groups 15-18 and periods 1-6 (P1-P6), computed at BP86/QZ4P//BP86/TZ2P (upper), and the corresponding proton affinities PA (at 298 K), computed at BP86/ QZ4P//BP86/TZ2P (lower).
K yield a relatively small (but not entirely constant) contribution -T∆acidS298 of -10 to -7 kcal/mol for 298 K. As a consequence, the Gibbs free energies ∆acidG298 show the same trends as the corresponding MCA values. The above trends in MCAs of neutral maingroup-element hydrides XHn are again similar to those in PAs that we found earlier (compare Figure 2, upper with lower).20 The most important difference is the overall lower MCA compared to the PA. 3.4. Correlation between Methyl Cation Affinities and Proton Affinities. Our computed MCA values are plotted against the corresponding PA values (see Table S3 and S4 in the Supporting Information) in Figure 3. We find a satisfactory correlation between the computed MCA and PA values of the combined set of neutral and anionic maingroup-element hydrides, which span a range of some 400 kcal/mol in PA values (see Figure 3). The corresponding linear relationship is shown
The slope of 0.895 for the linear MCA vs PA equation is somewhat smaller than unity and the intercept with x-axis occurs at PA ) 62 kcal/mol. As pointed out by Brauman et al.,6,26 a linear MCA versus PA plot with a nonzero intercept and unit slope is consistent with group additivity. The value of a nonunity slope expresses the difference in bonding abilities between the methyl cation and the proton. Furthermore, our present analyses confirm that the steric (Pauli) repulsion systematically increases from proton (no steric repulsion) to methyl cation (has steric repulsion) and that it is responsible for the corresponding decrease in affinity for these cations (see, e.g., Figures 1 and 2). This is reflected by the nonzero x-axis intercepts (at ca. 62 kcal/mol) in our linear MCA vs PA relationship in eqs 6. 4. Conclusion Methyl cation affinities (MCA) of archetypal bases XHn-1and XHn [i.e., (deprotonated) maingroup-element hydrides] in the gas phase correlate well in a linear relationship with the corresponding proton affinities. This follows from our relativistic density functional calculations, at BP86/QZ4P//BP86/TZ2P. The MCA values are systematically lower than the corresponding PA values. Bonding analyses show that this is due to an increased steric (Pauli) repulsion if one goes from proton (no steric repulsion) to methyl cation (has steric repulsion). Consequently, the trends in MCA values that result if one varies the bases across the periodic table are very similar to the corresponding trends in PA values. Thus, all methyl cation
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affinities decrease along the second-period bases as the valence 2p AOs of the Lewis-basic atom X become more compact and stable (i.e., along CH3-, NH2-, OH-, and F- and also along NH3, OH2, FH, and Ne). This nicely agrees with analyses by Bartmess and Hinde who ascribe the weakening in PA along CH3-, NH2-, OH-, and F- to a reduction in the electron reorganization enthalpy on formation of the conjugate acid.27 This well-known trend changes if one descends in the periodic table to higher periods. The methyl cation affinity of the bases decreases down the most left group (i.e., group 14 for XHn-1-, and group 15 for XHn), whereas it changes less in the groups more to the right in the periodic table. This causes the methyl cation affinities along higher-period bases to first increase and then to decrease again until group 18. Acknowledgment. We thank Dr. Juan M. Ruiz for sharing his computed PA values and the National Research School Combination-Catalysis (NRSC-C) and The Netherlands Organization for Scientific Research (NWO-CW and NWO-NCF) for financial support. Supporting Information Available: Energy decomposition analyses (EDA), PA values, and Cartesian coordinates of all species occurring in this study. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Smith, M. B.; March, J. March’s AdVanced Organic Chemistry; Wiley-Interscience: New York, USA, 2007. (2) Wade, Jr. L. G.; Organic Chemistry; Pearson/Prentice Hall: Upper Saddle River, New Jersey, USA, 2005. (3) Born, M. Z. Phys. 1920, 1, 45. (4) Onsager, L. J. Am. Chem. Soc. 1936, 58, 1486. (5) Uggerud, E. Eur. J. Mass Spectrom. 2000, 6, 131. (6) Brauman, J. I.; Han, C.-C. J. Am. Chem. Soc. 1988, 110, 5611. (7) McMahon, T. B.; Heinis, T.; Nicol, G.; Hovey, J. K.; Kebarle, P. J. Am. Chem. Soc. 1988, 110, 7591. (8) Deakyne, C. A.; Meot-Ner, M. J. Phys. Chem. 1990, 94, 232. (9) McMahon, T. B.; Kebarle, P. Can. J. Chem. 1985, 63, 3160. (10) Baerends, E. J.; Autschbach, J.; Bashford, D.; Be´rces, A.; Bickelhaupt, F. M.; Bo, C.; Boerrigter P.M.; Cavallo, L.; Chong, D. P.; Deng, L.; Dickson, R. M.; Ellis, D. E.; van Faassen, M.; Fan, L.; Fischer, T. H.; Fonseca Guerra, C.; Ghysels, A.; Giammona, A.; van Gisbergen, S. J. A.; Go¨tz, A. W.; Groeneveld, J. A.; Gritsenko, O. V.; Gru¨ning, M.; Harris, F. E.; Harris, P.; van den Hoek, P.; Jacob, C. R.; Jacobsen, H.; Jensen, L.; Van Kessel, G.; Kootstra, F.; Krykunov, M. V.; van Lenthe, E.; McCormack, D. A.; Michalak, A.; Mitoraj, M.; Neugebauer, J.; Nicu, V. P.; Noodleman, L.; Osinga, V. P. Patchkovskii, S.; Philipsen, P. H. T.; Post, D.; Pye, C. C.; Ravenek, W.; Rodriguez, J. I.; Ros, P.; Schipper, P. R. T.; Schreckenbach, G.; Seth, M.; Snijders, J. G.; Sola`, M.; Swart, M.; Swerhone, D.; te Velde, G.; Vernooijs, P.; Versluis, L.; Visscher, L.; Visser, O.; Wang, F.; Wesolowski, T. A.; van Wezenbeek, E. M.; Wiesenekker G.; Wolff, S. K.; Woo, T. K.; Yakovlev, A. L.; Ziegler, T. ADF2008.01, SCM, Theoretical Chemistry; Vrije Universiteit: Amsterdam, The Netherlands; http://www. scm.com.
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